convergence rates of solutions for n-dimensional quasilinear damped wave equation

We realize the asymptotic profile for the solutions to the n-dimensional quasilinear damped wave equation in the divergence form is the solution of the corresponding linear parabolic equation with special initial data, and we further show the L p ( 1 ⩽ p ⩽ ∞ ) (in particular, p = 1 ) convergence rates to this linear asymptotic profile.